【作者】 陶芮；

【导师】 商朋见；

【作者基本信息】 北京交通大学 ， 应用数学， 2011， 硕士

【摘要】 标度不变性对于复杂系统的研究越来越受到学者们的重视,而近年来测定复杂动态时间序列的标度化指数主要都是一些基于方差计算的方法,这些方法可以很好的测定那些方差有限的序列,而对于方差无限或者不存在的序列却无能为力。然而在很多复杂系统中的时间序列都可能有无限方差或是方差不存在的情况,本文将主要致力于基于时间序列产生的扩散过程熵的统计分析方法和基于累积概率的统计方法进行探讨和研究。这两种方法都可以很好的测定方差无限或者不存在的序列。在本文中,首先对于扩散熵分析法(DEA)的盒子过程我们讨论了其算法的改进,然后讨论了扩散熵分析法与概率流分析法(PFA)在高斯模型和勒维模型中的差异。之后尝试使用经验模式分解(EMD)与这两种方法结合,再将结合后的方法应用在高斯模型和勒维模型中。比较结合前后两种方法在两种模型中的差异,讨论其特性。将研究得出的结果应用于实际的股票数据中,研究股票指数的标度特性,从而进一步研究股票指数的统计特性。更多还原

【Abstract】 The study of scale invariance has been payed more and more attention to for complex systems. The methods currently used to determine the scaling exponent of a complex dynamic time series are based on numerical evaluation of variance. That means all this methods can be safely applied to the case where the variances are finite but fail to determine the scaling exponent when the variances are infinite or don’t exit. Most time series of the complex dynamic system have infinite variances or don’t have variances. In this paper we study a statistic method based on the Shannon entropy of the diffusion process generated by a time series and a statistic method based on the cumulative probabilities. Both methods can well determine the scaling exponent of the series with infinite variances or without variances. In this paper, first we will improve the binning algorithm of the diffusion entropy analysis. And then we will discuss the distinction between diffusion entropy analysis and probability flux analysis applied to Guass model and Levy model. We then try to combine empirical mode decompose and the two methods separately. After the combination we apply the two methods to Guass model and Levy model. We study the differences between before and after the combination. We use the conclusions to study the scaling properties and statistic properties of the stocks index datas.更多还原